beatricalwu

2022-07-19

Geometric Sequence with Normal Distribution Problem
The running time (in seconds) of an algorithm on a data set is approximately normally distributed with mean 3 and variance 0.25.
a. What is the probability that the running time of a run selected at random will exceed 2.6 seconds?
Answer for (a): I've computed this and found it to be $p=0.7881.$.
b. What is the probability that the running time of exactly one of four randomly selected runs will exceed 2.6 seconds?
Answer for (b): Not sure, I know it's a geometric sequence and I believe the formula that I need to use to be $p\left(1-p{\right)}^{3}$, thus giving me $0.7881\left(1-0.7881{\right)}^{3}$ however this was marked incorrect. I'm trying to figure out why, can someone explain my error and how to arrive at the correct solution?

nuramaaji2000fh

Expert

Step 1
You have 4 choices for which run will exceed 2.6 seconds. So your answer should be $4p\left(1-p{\right)}^{3}$ instead of $p\left(1-p{\right)}^{3}$.
Step 2
You basically calculated the probability that a pre-determined run will exceed 2.6 seconds, and the other 3 runs are less than 2.6 seconds.

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